%0 Journal Article
%T Vacuum Nodes and Anomalies in Quantum Theories
%A M. Aguado
%A M. Asorey
%A J. G. Esteve
%J Mathematics
%D 2000
%I arXiv
%R 10.1007/s002200100390
%X We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple geometric terms. We analyse in detail two different archetypical systems: i) a planar rotor with a non-trivial magnetic flux $\Phi$, ii) Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any reflection invariant potential $V$ is encoded in the nodal structure of the unique vacuum for $\theta=\pi$. In the second case we prove that the nodes of the first Landau level for unit magnetic charge appear at the crossing of the two non-contractible circles $\alpha_-$, $\beta_-$ with holonomies $h_{\alpha_-}(A)= h_{\beta_-}(A)=-1$ for any reflection invariant potential $V$. This property illustrates the geometric origin of the quantum translation anomaly.
%U http://arxiv.org/abs/hep-th/0010227v1